I work for Verizon and YES you can use another CDMA's carrier on Verizon. As far as using a VZW phone on Sprint, unless you know someone that can reprogram it, it's not gonna happen. I USE to work for Sprint and they have this "if it doesn't say Sprint, we won't allow it" policy.
Verizon has a request sheet if you want to use your CDMA phone on verizon. You have to fill it out and send it in with your phone. They say it takes a few weeks to get it back all programmed for VZW. I've never tried it but I know people have done it. They usually program phones that they already carry, like Sprint Touch Pro to Verizon Touch Pro.. all they did was flash the rom for Verizon and etc. I uploaded the form on here somewhere.
Hope this helps